Differential and Integral Calculus

Course Information

College	Anan College	Year	2024
Course Title	Differential and Integral Calculus
Course Code	1113A01	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Liberal Arts and Sciences	Student Grade	3rd
Term	Year-round	Classes per Week	前期:2 後期:2
Textbook and/or Teaching Materials	新版 微分積分 (New Edition Mathematics Series, Differential and Integral), Kazuo Okamoto, Jikkyo shuppan; 「改訂版　チャート式 基礎と演習 数学 Ⅲ」(Revised edition Chart. Foundations and Exercises Mathematics III), Suken shuppan; 「はぎ取り式練習ドリル　Ⅲ」(Practice drill Ⅲ), Suken shuppan.
Instructor	Tagami Takanori,Kushida Masahiro,Yamada Kohtaro,Nishimori Yasuhito,Ukida Takuya

Course Objectives

1. Students are able to find the area and volume by using definite integrals.
2. Students are able to calculate the iterated integrals.
3. Students are able to calculate partial derivatives.
4. Students are able to solve first-order differential equations.
5. Students are able to solve second-order differential equations.

Rubric

	Ideal Level	Standard Level	Minimum Level
Achievement 1	Be able to find complex area and volume by using definite integrals.	Be able to find standard area and volume by using definite integrals.	Be able to find simple area and volume by using definite integrals.
Achievement 2	Be able to calculate complex iterated integrals.	Be able to calculate standard iterated integrals.	Be able to calculate basic iterated integrals.
Achievement 3	Be able to calculate complex partial derivatives.	Be are able to calculate standard partial derivatives.	Be able to calculate basic partial derivatives.
Achievement 4	Be able to solve complex first-order differential equations.	Be able to solve standard first-order differential equations.	Be able to solve basic first-order differential equations.
Achievement 5	Be able to solve complex second-order differential equations.	Be able to solve standard second-order differential equations.	Be able to solve basic second-order differential equations.

Assigned Department Objectives

学習・教育到達度目標 B-2 （数学に関する知識を用いて問題解決に取り組める。）

Teaching Method

Outline:

Mathematics is the most necessary subject of Anan College. This course focuses on Calculus: differentiation and integration. In order to analyze functions and measure area and volume, students acquire knowledge and skills of calculus. They will gain the basic concept of partial differentials and iterated integrals.

Style:

According to the textbooks, steudents learn the basic concepts and explain techniques of calculation. Students practice calculous by drill, chart and workbook.
【Lecture: 60 hours】

Notice:

1. Students will concentrate in class and establish efficient learning methods. Preparation and review are required.
2. Students will make effort for regular exams, quizzes and homework.
3. Strictly observe the deadline for submission of homework.

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Differentiation review	Calculate basic differentiation; product and quotient rule; chain rule of differentiation.
		2nd	Integration review	Calculate basic indefinite and definite integrals.
		3rd	Applications of integration (part I)	By using integrals, calculate the area between curves and volume of rotating body.
		4th	Applications of integration (part II)	By using integrals, calculate the length of curves.
		5th	Indefinite integral (part I)	Calculate indefinite integrals of trigonometric rational expressions.
		6th	Indefinite integral (part II)	Calculate indefinite integrals of irrational functions.
		7th	Review and exercises
		8th	Mid-Term Exam
	2nd Quarter
		9th	Improper integral	Calculate basic improper integrals.
		10th	Iterative integral (part I)	Calculate basic iterative integrals.
		11th	Iterative integral (part II)	Calculate standard iterative integrals.
		12th	Change the order of iterative integration (part I)	Change the order of iterative integration on simple domain.
		13th	Change the order of iterative integration (part II)	Change the order of iterative integration on standard domain.
		14th	Change of variables in iterative integration (part I)	By using linear transformation, find iterative integration
		15th	Change of variables in iterative integration (part II)	By using linear transformation and polar transformation, find iterative integration.
		16th	Review and exercises
2nd Semester
	3rd Quarter
		1st	Partial derivative and Partial differentiation	Calculate partial derivative and partial differentiation.
		2nd	Extreme value problem	By using the criterion of the extreme value, find extreme values.
		3rd	Extreme value problem for two-variable functions	By using the criterion of the extreme value, find extreme values for two-variable functions.
		4th	Infinite series and Taylor series	Introduction to infinite series. Give Taylor series for trigonometric functions and exponential functions.
		5th	Linear differential equation of first order (separation of variables)	Solve linear differential equations of first order, by separation of variables.
		6th	Homogeneous differential equation	Solve homogeneous differential equations of first order.
		7th	Review and exercise
		8th	Mid-Term Exam
	4th Quarter
		9th	Linear differential equation of first order (non-homogeneous)	Introduction to variation of parameters/the method of undetermined coefficients.
		10th	Linear differential equation of second order (part I)	Introduction to reduction of order.
		11th	Linear differential equation of second order (part II)	Solve differential equations of second order, by reduction of order.
		12th	Linear differential equation of second order with constant coefficients (homogeneous)	Solve linear differential equations of second order, by solving auxiliary equation,
		13th	Linear differential equation of second order with constant coefficients (non-homogeneous) I	Find the general solution, when the non-homegeneous term is a polynomial.
		14th	Linear differential equation of second order with constant coefficients (non-homogeneous) II	Find the general solution, when the non-homegeneous term is an exponential.
		15th	Linear differential equation of second order with constant coefficients (non-homogeneous) III	Find the general solution, when the non-homegeneous term is sin or cos.
		16th	Review and exercise

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Homework	Total
Subtotal	70	0	0	0	0	30	100
Basic Proficiency	70	0	0	0	0	30	100
Specialized Proficiency	0	0	0	0	0	0	0
Cross Area Proficiency	0	0	0	0	0	0	0